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Explore a 15-minute conference talk presented at VMCAI'24 that introduces TP-DejaVu, an innovative runtime verification tool. Delve into the challenges of maintaining low incremental complexity while enhancing the expressive power of specification formalisms in runtime verification. Discover how TP-DejaVu combines two methodologies to efficiently handle specifications involving data, arithmetic operations, and comparisons. Learn about the two-phase approach that allows for processing events with data across arbitrary distances in observed executions. Gain insights into how this tool extends the capabilities of the original DejaVu, offering a more comprehensive solution for runtime verification challenges.